TWoK indeed makes quite a bit of effort to show that time has passed, in terms of multiple direct references and inferences. TMP is more neutral on that - the characters are clearly older physically, but only moderately higher in rank, and the absences of Spock and McCoy feel like brief stints to the alien world outside Starfleet rather than valid career choices. One might even think that the minimum time since TOS that we learn from the dialogue, 2.5 years, is in fact the entire time that has transpired.
Yet it never was a comfortable fit. Why is Kirk a Rear Admiral now, and the bloody Chief of Ops to boot? Did they skip Commodore when promoting him for his heroics? Also, yes, this is an ambitious motion picture and no longer a TV show - but in-universe, how come everything looks so very different? Are we to think in terms of "a universe" or not?
TWoK is unabashed about referring back to the TV show, with characters and events and concepts. TMP is quite abashed, despite basically doing the very same. Even when Trek moves on, along the track laid down with the second movie, and truly becomes a universe and a franchise, we're left wondering about TMP.
Plopping TMP in a slot closer to the fictional 2280 than 2270 helps with the rank issues, gives more depth to the homecomings of Spock and McCoy, and excuses Kirk becoming such an ass when separated from his friends and his true love. But remembering TMP eats away at the impact of TWoK, which retreads the frustrations of "Admiral Kirk".
Then again, the double whammy nicely drives home the point: Kirk's love will forever go unrequited and unfulfilled, since whenever he gives his all to Starfleet, it takes him farther away from what Starfleet could give to him. There's no winning that particular game, except by throwing it, as in the later movies. The rank stagnation becomes a big part of Kirk's character, and nicely culminates in him bowing out as an unwanted dinosaur who would have been even more of an embarrasment and hindrance to peace with Klingons had he retained high rank till the end.
Timo Saloniemi